DIFFERENTIAL EQUATIONS SM212 / SM212P SPRING SEMESTER 2005-2006 Textbook: Fundamentals of Differential equations, 6th ed., by R. K. Nagle, E. B. Saff, A. D. Snider, Addison-Wesley (Pearson), 2004. Certain lessons in this syllabus are marked CP under the page heading. For these lessons, your instructor may ask you to use Maple or the TI Voyage 200 or another software package to solve and plot, by numerical means, the indicated problem. Many problems need to be solved and plotted by numerical means since these problems may not have an explicit solution written as elementary functions. These problems may help you understand the usefulness of the numerical approach. LESSON/PAGES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 1-5 6-11 16-21 24-27 127-129 40-45 49-54 TOPICS PROBLEMS p. 5: 1,4,8,11,15,16 p.14: 3,6,10,11,20(a),22 p.22: 1,3,4,5,6 p.28: 2,5CP,6CP,15CP p.132: 7,8CP p.46: 4,5,6,7,10,12,18,34 p.54: 2,3,7,9,10,19,21 p.98: 1 p.107: 1,5 p.115: 1,2,7 p.122: 1,3,4
1.1 Definitions and terminology 1.2 Solutions and IVPs 1.3 Direction Fields / Isoclines 1.4 Numerical solutions: Euler's method 3.6 Numerical solutions: Improved Euler 2.2 Separable DEs 2.3 Linear DEs review 89-91(ex.1) 3.2 Applications (mixing) & 101-103(ex.1) 3.3 Applications (heating/cooling) 108-113 3.4 Applications (Newtonian mechanics) 119-122 3.5 Applications (Electrical circuits) review TEST 1 160-165 165-167& 326-329 169-173 328-329 179-187 333-337 4.2 4.2 6.2 4.3 6.2 4.4 6.3 2nd order linear homog. DEs Homogeneous w/const. coeffs cont'd 2nd order homog DEs, complex roots Higher order DEs Undeter. Coeffs. w/Annihilators, Superposition Undeter. Coeffs. w/Annihilators, Superposition
20. 154-155, 210-213 21. 213-219 22. 220-222, 224-225 23. 286-288 24. 25. 26. 351-355 27. 360-364 28. 366-370 29. 370-374 30. 376-380 31. 384-390 32. 384-390 33. 286-292, 414-416 34. 241-20 35. 253-260 36. 279-284 37. 38.
4.1, 4.8 Springs (undamped) 4.8 Springs (damped) 4.9 Springs (Forced) 5.6 Circuits (example 1) review TEST 2 7.2 Laplace Transform (LT) 7.3 Properties of LTs 7.4 Inverse LTs 7.4 Inverse LTs, partial fractions 7.5 IVPs by LTs 7.6 Unit step functions 7.6 Unit step functions (cont’d) 5.6 & 7.9 Electrical networks using Laplace 5.1 & 5.2 Mixing problems using Laplace 5.3 First order systems and Euler's method 5.5 Coupled Mass - Spring Systems by Laplace review review
p.167: 1,4,7,13,20,22 p.167: 9,11 & p. 331: 1,3,8,11 p.177: 1,5,10,23,28CP p.177: 2,15; p331:6,15,16 p.186: 1,5,9,11; p192: 2 p.186: 16; p192: 9,25; p. 337: 5,31 p.219: 1,2,3 p.219: 7,8,9 p.227: 3,9 p.291: 1,2,3
p.359: 1,4,12,13,17,20 p.365: 1,7,10,16,25 p.374: 1,2,3,6,8,9,11,19 p.374: 21,23,25,28 p.383: 1,4,7,23,25 p.395: 1,2,4,5,8 p.395: 11,19,29,30 p.416: 23, 24 p.251: 31 p.261: 1,5,10CP,11CP p.284: 1,6
39. 40. 41. 42. 43. 44. 45.&46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57-59. 503-507 508-511 512-521 524-530 533-541 579-583 576-583 589-596 596-602 607-611 580-583 612-615.
review TEST 3 9.1 9.2 9.3 9.4 9.5 Matrix form for systems Linear algebraic equations / rref Matrix algebra/inverse matrices/determinants Linear systems in normal form Linear systems with const coeffs Eigenvalues & eigenvectors p.507: 1,4,8,11 p.512: 1,8,11,12b p.521: 2,4,6,13,25 p.532: 1,5,10,23 p. 541: 11,13,31,45 p.587: 3,9,15,23 p.587: 17,25,33 p.603 9,11,17,19 p.603 2,5,7,10,16,24 p.611: 5,11 p.624: 1 p.624: 3
10.2 Separable PDEs 10.2 Heat Equation 10.3 Fourier series define period, sine and cosine series 10.3 Convergence, odd & even functions 10.4 Sine & cosine series 10.5 Heat equation, zero ends 10.5 Heat equation, insulated ends review review TEST 4 review for final examination
The following web pages, created by Prof David Joyner and others, contain useful information relating to the course material: For hints on using the TI Voyage 200 see http://cadigweb.ew.usna.edu/~wdj/teach/sm212_ti92.html The Maple code at http://cadigweb.ew.usna.edu/~wdj/teach/sm212/sm212_euler.htm helps with the CPs in sections 1.4 and 3.6. The Maple code at http://cadigweb.ew.usna.edu/~wdj/teach/sm212/sm212_euler_2x2.html helps with the CPs in section 5.3. jmd@usna.edu last updated 12-20-2005